A Complete Physics Resource for preparing IIT-JEE,NEET,CBSE,ICSE and IGCSE. All Physics topics are divided into multiple sub topics and are explained in detail using concept videos and synopsis.Lots of problems in each topic are solved to understand the concepts clearly.

Monday, November 10, 2014

Kinetic theory of gases and Expression for Pressure

The purpose of the Kinetic theory
of the gases is to link to the macroscopic properties of the gases like
pressure volume,temperature with the macroscopic properties of the gas
molecules like displacement,velocity, momentum, force and kinetic energy.

To apply the connect theory of
the gases to the molecules we shall make some assumptions.

1. We shall assume that the size
of the molecule is very small and when compared with the volume of the gas
occupied the volume of the gas molecules occupied is negligible.

2. The gas molecules are tiny in
size , spherical in shape , neutral with respect to charge and all are
identical.

3. The molecules moves in all directions randomly with all possible
speeds.

4. The collision of the gas molecules
is an elastic. That means during the collision both momentum and kinetic energy
are conserved. There is no wastage of energy in the format of sound light and
heat.

Mean free path:

The average distance molecule can
travel without colliding the neighboring molecules is called as mean free
path.When the molecule starts its journey, its motion is so random under
regular that the we cannot predict what is going to be its path is. In between
any of the two collisions, the molecule travel some distance and by measuring this
total distances and by dividing it with the number of the collisions we can calculate the value
of the mean free path.

The gas which obeys all gas laws
at all temperatures and pressures is called an ideal gas. In reality no gas is actually Ideal and all the existing gases are called real gases.While
explaining kinetic theory of the gases, anyway we assume that the gas is Ideal.

Practically real gas obeys all gas laws only at high temperatures and low pressures.

Expression of the pressure of an
ideal gas:

Being the gas molecules are
having collisions among themselves and with the walls of the container, they
are going to exert some pressure and
here we are going to calculate that pressure. Let us consider a container who is having cube shape. Let the side of the cube is L and
a gas molecule of mass m is moving in parallel to YZ plane along the x-axis.

As the collision is elastic the
molecule will come back with the same velocity.Thus we can calculate the
change of the momentem with respect to time which leads the calculation of the
force. The derivation for the pressure is made are shown below.

This can be further continued by writing all the forces and then further writing equation for the pressure as defined as the force per unit area as shown further.

The expression for the pressure
of a gas molecule can be expressed in terms of kinetic energy of the gas
molecule also. Here RMS velocity of the gas molecule can be expressed as the root mean square velocity of the gas
molecule. Basing the ideal gas equation even we can measure the impact of the
temperature here. The temperature at which the RMS velocity of gas molecule becomes zero is called a
absolute zero temperature and that is taken as a reference to define Kelvin
scale.

We can further find a relation between temperature of the gas and the RMS velocity of the gas molecule as shown below.We can also define a particular temparatue at which RMS velocity of gas molecule become zero called absolute temperature.